Finite Group Databasebeta

← #15754597

Subgroups — #15754597

Order 3328.

844 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114926C212yesmaximal, complemented
2#13114824C211yesmaximal, characteristic, complemented
3#13113404C212yesmaximal, complemented
4#13113154C211yesmaximal, characteristic, complemented
5C2×C13×#553C211yesmaximal, characteristic
6C13×#553—24no—
7C13×#553—24no—
8C2×C13×#126—21no—
9C2×C13×#125C411yescharacteristic, complemented
10C2×C13×#123—21no—
11C2×C13×#121—21no—
12C2×C13×#121C411yescharacteristic, complemented
13C2×C13×#121C2211yescharacteristic
14C2×C4×D4×C13—21no—
15C2×C4×D4×C13C411yescharacteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17C2×C13×#117C411yescharacteristic, complemented
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88074—21no—
20#11718873C2212yes—
21C2×C22⋊#1055C2212yes—
22#11718129—24no—
23#11718121—24no—
24#11718120—21no—
25#11718118—21no—
26#11718117—21no—
27C22×D4×C13—21no—
28C22×D4×C13—21no—
29C22×D4×C13C2×C411yescharacteristic
30C22×D4×C13D411yescharacteristic
31C23×C4×C13—21no—
32C23×C4×C13—21no—
33C23×C4×C13C2×C411yescharacteristic
34C23×C4×C13C2311yescharacteristic
35C13×#126—28no—
36C13×#125—22no—
37C13×#125—22no—
38C13×#123—28no—
39C13×#121—28no—
40C13×#121—22no—
41C13×#121—22no—
42C13×#121—22no—
43C13×#121D414yes—
44C4×D4×C13—28no—
45C4×D4×C13—22no—
46C4×D4×C13—22no—
47C4×D4×C13—22no—
48C4×D4×C13—22no—
49C13×#117—22no—
50C13×#117—22no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—21no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4C2×C411yescharacteristic
56C2×C13×C4⋊C4C2×C411yescharacteristic
57C2×C13×C4⋊C4C2×C411yescharacteristic
58C2×C13×C4⋊C4D411yescharacteristic
59C2×C13×C4⋊C4D414yes—
60C2×C13×C22⋊C4—21no—
61C2×C13×C22⋊C4—21no—
62C2×C13×C22⋊C4—21no—
63C2×C13×C22⋊C4—21no—
64C2×C13×C22⋊C4D411yescharacteristic
65C2×C13×C22⋊C4D411yescharacteristic
66C2×C42×C13—21no—
67C2×C42×C13C2×C411yescharacteristic
68C2×C22⋊Dic13—22no—
69C2×C4⋊Dic13—22no—
70C22×#1055—22no—
71#88074—42no—
72#88071—22no—
73C22⋊#1055—22no—
74C22⋊#1055—22no—
75#8378—131nomaximal, Sylow
76C24×C13—21no—
77C24×C13C22⋊C411yescharacteristic
78C24×C13C2×D411yescharacteristic
79C2×D4×C13—22no—
80C2×D4×C13—24no—
81C2×D4×C13—22no—
82C2×D4×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13—24no—
85C2×D4×C13—21no—
86C2×D4×C13—42no—
87C2×D4×C13—42no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—82no—
91C2×D4×C13C22⋊C412yes—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—24no—
96C22×C4×C13—24no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—42no—
100C22×C4×C13—42no—
101C22×C4×C13—82no—
102C22×C4×C13—82no—
103C22×C4×C13C22⋊C411yescharacteristic
104C22×C4×C13C22⋊C411yescharacteristic
105C22×C4×C13C22⋊C411yescharacteristic
106C22×C4×C13C22×C411yescharacteristic
107C22×C4×C13C2×D412yes—
108C22×C4×C13C2×D412yes—
109C22×C4×C13C2×D411yescharacteristic
110C22×Dic13—42no—
111C13×C4⋊C4—24no—
112C13×C4⋊C4—24no—
113C13×C4⋊C4—21no—
114C13×C4⋊C4—21no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—24no—
117C13×C4⋊C4—22no—
118C13×C4⋊C4C22⋊C412yes—
119C13×C4⋊C4C22⋊C412yes—
120C13×C4⋊C4C22⋊C412yes—
121C13×C22⋊C4—24no—
122C13×C22⋊C4—24no—
123C13×C22⋊C4—24no—
124C13×C22⋊C4—22no—
125C13×C22⋊C4—24no—
126C13×C22⋊C4—22no—
127C42×C13—24no—
128C42×C13—21no—
129C42×C13—21no—
130C22⋊Dic13—42no—
131C22⋊Dic13—42no—
132C4⋊Dic13—44no—
133C2×#1055—44no—
134C2×#1055—42no—
135C2×#553D1311yescharacteristic
136#1824—132no—
137#1799—131no—
138#1519—132no—
139#1459—131no—
140C23×C13—21no—
141C23×C13—22no—
142C23×C13—21no—
143C23×C13—21no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13—42no—
147C23×C13—42no—
148C23×C13—41no—
149C23×C13—41no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13C2×C22⋊C411yescharacteristic
153C23×C13#12012yes—
154C23×C13#13512yes—
155C23×C13AGL(1,ℤ/8)11yescharacteristic
156C23×C13#13711yescharacteristic
157D4×C13—42no—
158D4×C13—42no—
159D4×C13—44no—
160D4×C13—42no—
161D4×C13—44no—
162D4×C13—42no—
163D4×C13—84no—
164C2×C4×C13—24no—
165C2×C4×C13—22no—
166C2×C4×C13—21no—
167C2×C4×C13—21no—
168C2×C4×C13—22no—
169C2×C4×C13—21no—
170C2×C4×C13—22no—
171C2×C4×C13—22no—
172C2×C4×C13—21no—
173C2×C4×C13—21no—
174C2×C4×C13—41no—
175C2×C4×C13—42no—
176C2×C4×C13—42no—
177C2×C4×C13—42no—
178C2×C4×C13—42no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—42no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—84no—
185C2×C4×C13—84no—
186C2×C4×C13C2×C22⋊C411yescharacteristic
187C2×C4×C13C2×C22⋊C411yescharacteristic
188C2×C4×C13#12012yes—
189C2×Dic13—82no—
190C2×Dic13—82no—
191C2×Dic13—82no—
192#1055—82no—
193#553—24no—
194#553—24no—
195C2×#126—21no—
196C2×#125Dic1311yescharacteristic, complemented
197C2×#123—21no—
198C2×#121—21no—
199C2×#121Dic1311yescharacteristic, complemented
200C2×#121C2×D1311yescharacteristic
201C2×C4×D4—21no—
202C2×C4×D4Dic1311yescharacteristic, complemented
203C2×C4×D4C2×D1311yescharacteristic
204C2×#117Dic1311yescharacteristic, complemented
205C22×C4⋊C4C2×D1311yescharacteristic
206C2×#99—261no—
207C2×C22⋊C8—132no—
208#380—132no—
209#342—261no—
210#340—264no—
211#327—264no—
212#324—261no—
213#323—261no—
214C22×C13—22no—
215C22×C13—21no—
216C22×C13—22no—
217C22×C13—21no—
218C22×C13—42no—
219C22×C13—41no—
220C22×C13—41no—
221C22×C13—42no—
222C22×C13—41no—
223C22×C13—41no—
224C22×C13—42no—
225C22×C13—41no—
226C22×C13—42no—
227C22×C13—81no—
228C22×C13—81no—
229C22×C13—82no—
230C22×C13—82no—
231C22×C13#37911yescharacteristic
232C22×C13#41611yescharacteristic
233C22×C13#41711yescharacteristic
234C22×C13#44912yes—
235C22×C13#45212yes—
236C4×C13—22no—
237C4×C13—21no—
238C4×C13—42no—
239C4×C13—42no—
240C4×C13—41no—
241C4×C13—41no—
242C4×C13—41no—
243C4×C13—42no—
244C4×C13#41012yes—
245Dic13—162no—
246C22×D4—21no—
247C22×D4—21no—
248C22×D4C2×Dic1311yescharacteristic
249C22×D4C22⋊D1311yescharacteristic
250C23×C4—21no—
251C23×C4—21no—
252C23×C4C2×Dic1311yescharacteristic
253C23×C4C22×D1311yescharacteristic
254C22×C8—262no—
255#126—28no—
256#125—22no—
257#125—22no—
258#123—28no—
259#121—28no—
260#121—22no—
261#121—22no—
262#121—22no—
263#121C22⋊D1314yes—
264C4×D4—28no—
265C4×D4—22no—
266C4×D4—22no—
267C4×D4—22no—
268C4×D4—22no—
269#117—22no—
270#117—22no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—262no—
276C2×C4⋊C4C2×Dic1311yescharacteristic
277C2×C4⋊C4C2×Dic1311yescharacteristic
278C2×C4⋊C4C2×Dic1311yescharacteristic
279C2×C4⋊C4C22⋊D1311yescharacteristic
280C2×C4⋊C4C22⋊D1314yes—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—262no—
286C2×C22⋊C4C22⋊D1311yescharacteristic
287C2×C22⋊C4C22⋊D1311yescharacteristic
288C2×C42—21no—
289C2×C42C2×Dic1311yescharacteristic
290#99—522no—
291C22⋊C8—262no—
292C22⋊C8—262no—
293#95—262no—
294C2×C13—22no—
295C2×C13—21no—
296C2×C13—21no—
297C2×C13—22no—
298C2×C13—81no—
299C2×C13—82no—
300C2×C13#178211yescharacteristic
301C2×C13#178811yescharacteristic
302C2×C13#179511yescharacteristic
303C24—21no—
304C24C22⋊Dic1311yescharacteristic
305C24C2×C22⋊D1311yescharacteristic
306C2×D4—21no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—22no—
310C2×D4—24no—
311C2×D4—24no—
312C2×D4—21no—
313C2×D4—42no—
314C2×D4—41no—
315C2×D4—42no—
316C2×D4—41no—
317C2×D4—82no—
318C2×D4C22⋊Dic1312yes—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—24no—
323C22×C4—24no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—42no—
327C22×C4—42no—
328C22×C4—82no—
329C22×C4—82no—
330C22×C4—522no—
331C22×C4C22⋊Dic1311yescharacteristic
332C22×C4C22⋊Dic1311yescharacteristic
333C22×C4C22⋊Dic1311yescharacteristic
334C22×C4C22×Dic1311yescharacteristic
335C22×C4C2×C22⋊D1312yes—
336C22×C4C2×C22⋊D1312yes—
337C22×C4C2×C22⋊D1311yescharacteristic
338C2×C8—524no—
339C2×C8—522no—
340C4⋊C4—24no—
341C4⋊C4—24no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—24no—
346C4⋊C4—22no—
347C4⋊C4—524no—
348C4⋊C4C22⋊Dic1312yes—
349C4⋊C4C22⋊Dic1312yes—
350C4⋊C4C22⋊Dic1312yes—
351C22⋊C4—24no—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—22no—
355C22⋊C4—24no—
356C22⋊C4—22no—
357C22⋊C4—522no—
358C22⋊C4—522no—
359C42—24no—
360C42—21no—
361C42—21no—
362C13#837811yescharacteristic, complemented, Sylow
363C23—21no—
364C23—22no—
365C23—21no—
366C23—21no—
367C23—41no—
368C23—41no—
369C23—42no—
370C23—42no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—41no—
375C23#8820311yescharacteristic
376C23#8820412yes—
377C23#8820511yescharacteristic
378C23C2×C22⋊Dic1311yescharacteristic
379C23#8820712yes—
380D4—42no—
381D4—42no—
382D4—44no—
383D4—42no—
384D4—44no—
385D4—42no—
386D4—84no—
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—84no—
408C2×C4—84no—
409C2×C4—1042no—
410C2×C4—1042no—
411C2×C4—1042no—
412C2×C4C2×C22⋊Dic1311yescharacteristic
413C2×C4C2×C22⋊Dic1311yescharacteristic
414C2×C4#8820712yes—
415C8—1042no—
416C22—21no—
417C22—22no—
418C22—21no—
419C22—22no—
420C22—41no—
421C22—42no—
422C22—41no—
423C22—41no—
424C22—42no—
425C22—41no—
426C22—42no—
427C22—42no—
428C22—41no—
429C22—81no—
430C22—81no—
431C22—82no—
432C22—82no—
433C22#1171889311yescharacteristic
434C22#1171889411yescharacteristic
435C22#1171889912yes—
436C22#1171890012yes—
437C22#1171890811yescharacteristic
438C4—22no—
439C4—21no—
440C4—41no—
441C4—41no—
442C4—42no—
443C4—42no—
444C4—42no—
445C4—41no—
446C4—2082no—
447C4#1171890112yes—
448C2—22no—
449C2—21no—
450C2—21no—
451C2—22no—
452C2—82no—
453C2—81no—
454C2#1311475411yescharacteristic
455C2#1311477611yescharacteristic
456C2#1311480611yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
Fitting, prime radicalC2×C13×#553C2
socleC22×C13#379
cosocleC23×C4×C13C23
hypercenterC2×#553D13
hypocenterC13#8378
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#553

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13114926C2semidirect
2. #13114824C2semidirect
3. #13113404C2semidirect
4. #13113154C2semidirect
9. C2×C13×#125C4semidirect
12. C2×C13×#121C4semidirect
15. C2×C4×D4×C13C4semidirect
17. C2×C13×#117C4semidirect
196. C2×#125Dic13semidirect
199. C2×#121Dic13semidirect
202. C2×C4×D4Dic13semidirect
204. C2×#117Dic13semidirect
362. C13#8378semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131149262
#131148242
#131134042
#131131542
C2×C13×#5532
#837813